Geometry Level pending

In order to craft the INFINITE RASENGAN, one has to focus his chakra into a...:

...ball that is inscribed into a tetrahedron whose edges are equal to \(a\), so that it touches all edges of the tetrahedron.

It is said, that each unit of volume of the sphere that lies outside the tetrahedron holds unimaginable power, capable of smashing all things in the universe. Madara, being a crafty fox, found a way to redirect this energy to grant wishes instead, by using a floor function modification.

If the total volume of the sphere outside the tetrahedron equals \( R { a }^{ 3 }\sqrt { S } (E-N\sqrt { G } )AN\), then how many wishes may Madara have granted by the \(\left\lfloor RASENGAN \right\rfloor \)?

NOTE: Please use [SPOILER ALERT] before mentioning any content from Naruto manga.


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